To simulate unsteady flow through reaches and networks of open channels for water resources investigations involving water withdrawal effects, bridge location and design analyses, flood inundation, and tidal flushing. The model is well suited for simulation of regulated, tidal, or wind driven flows in upland or coastal open channel reaches or in a network of channels connected in a dendritic layout or looped pattern.

2. Description

The BRANCH model uses a four point, implicit, finite difference approximation of the unsteady flow equations. Flow equations are formulated to account for non-uniform velocity distributions through the momentum Boussinesq coefficient, to accommodate flow storage/conveyance separation, and to include wind shear on the water surface as a forcing function. The model employs a nonlinear, iterative matrix solution method with user specified tolerance controls. The implicit solution technique permits
computations at large time steps. The four point, finite difference scheme, with weighting factors for function values and their spatial derivatives, provides a high degree of flexibility for simulating diverse flow conditions in channels of variable cross-sectional properties. Channel branches can be numbered in any order and subdivision of branches into segments of unequal lengths is possible, thereby providing for the computation of flow at any location. The model accommodates tributary inflows and diversions as well as lateral overbank flows and includes a Lagrangian, particle tracking scheme for conservative solutes. It allows for user selectable, constant, functional, or tabular frictional resistance.

3. Input

Cross-sections are defined by piece-wise, linear relations that can be
manually prepared or interactively entered, processed, and formatted via the supporting Channel Geometry Analysis Program (CGAP). Initial flow conditions can be prescribed as observed, estimated, assumed, or previously
computed. Boundary conditions (water levels or discharges) can be
specified by equation, time-series values, or functional relations. Time series data can be input directly via formatted sequential files or
automatically retrieved from the supporting data bases of the Time Dependent Data System (TDDS) or the Water Data Management System (WDMS).TDDS facilitates data retrieval and transfer to the USGS/NWIS data base.
Input can be either in metric or inch-pound system of units.

4. Output

Time series of computed flow results can be output for selected locations as tables or graphs. Tables include results at each time step or iteration and daily summaries. Individual terms can be calculated at each time step or iteration, and particle tracks, and cumulative flow volumes
can be listed. Graphs include computed discharge or stage and computed versus measured discharge or stage.

5. Operational requirements and restrictions

BRANCH is coded in FORTRAN 77, making the program compatible with mainframe, workstation, and microcomputer systems and a variety of compilers. For microcomputers, a 32 bit processor (386 or higher) is needed. The code is easily dimensioned to allow use of the model for any channel configuration. Graphics output requires either a GKS or CalCOMP
graphics library. The time required (in seconds per day) for simulating the flow and movement of 8 conservative particles in a network of 25
branches with 69 cross-sections at a 15 minute time step is approximately 87s for a 16 MHz 386, 15s for a 16.7 MHz Data General AViiON workstation,10s for a 25 MHz Sun SPARCstation 1+, and 6s for a Cray X-MP/48.

6. Form of presentation

Scientific documentation and user guide are available in English (see reference below). Program, examples, and documentation are available on floppy disk and the Internet. The program is provided as executable code, but the source program is available on request. The BRANCH distribution includes the CGAP and TDDS programs, also written in FORTRAN 77. Training is conducted by the USGS.

7. Operational experience

BRANCH model use is extensive and worldwide. Currently, the model is
in operational use at nearly 40 sites as conducted by more than 12 USGS offices. The model has been in operational use since 1980.